document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1152726>Question 1152726</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If 0° < A, B < 90°, and sinA = cosB, compute cot(A+B) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #774811 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=774811\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28A%29+=+cos%28B%29 ALIGN=MIDDLE  ALT=\"sin%28A%29+=+cos%28B%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > if and only if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2BB+=+90 ALIGN=MIDDLE  ALT=\"A%2BB+=+90\"   DISABLED_style= \"max-width:90%; height:auto;\" >. We say that angles A and B are complementary\r<BR>\n" );
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document.write( "For example, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%2840%29+=+cos%2850%29 ALIGN=MIDDLE  ALT=\"sin%2840%29+=+cos%2850%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%2B50+=+90 ALIGN=MIDDLE  ALT=\"40%2B50+=+90\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using a calculator, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%2840%29+=+0.6427876 ALIGN=MIDDLE  ALT=\"sin%2840%29+=+0.6427876\"   DISABLED_style= \"max-width:90%; height:auto;\" > and  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%2850%29+=+0.6427876 ALIGN=MIDDLE  ALT=\"cos%2850%29+=+0.6427876\"   DISABLED_style= \"max-width:90%; height:auto;\" > (both approximate).\r<BR>\n" );
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document.write( "Because we are working with cotangent, let's start with the identity for tangent and rewrite it in terms of cotangent.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28x%29+=+sin%28x%29%2Fcos%28x%29 ALIGN=MIDDLE  ALT=\"tan%28x%29+=+sin%28x%29%2Fcos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28x%29%2F1+=+sin%28x%29%2Fcos%28x%29 ALIGN=MIDDLE  ALT=\"tan%28x%29%2F1+=+sin%28x%29%2Fcos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Ftan%28x%29+=+cos%28x%29%2Fsin%28x%29 ALIGN=MIDDLE  ALT=\"1%2Ftan%28x%29+=+cos%28x%29%2Fsin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Apply reciprocal to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot%28x%29+=+cos%28x%29%2Fsin%28x%29 ALIGN=MIDDLE  ALT=\"cot%28x%29+=+cos%28x%29%2Fsin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > We will use this later. Call this equation (1).\r<BR>\n" );
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document.write( "It might be tempting to use the reciprocal identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot%28x%29+=+1%2F%28tan%28x%29%29 ALIGN=MIDDLE  ALT=\"cot%28x%29+=+1%2F%28tan%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > but if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+90 ALIGN=MIDDLE  ALT=\"x+=+90\"   DISABLED_style= \"max-width:90%; height:auto;\" > degrees, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28x%29+=+0 ALIGN=MIDDLE  ALT=\"tan%28x%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, making <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28tan%28x%29%29 ALIGN=MIDDLE  ALT=\"1%2F%28tan%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to be undefined. Instead it is better to use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot%28x%29+=+cos%28x%29%2Fsin%28x%29 ALIGN=MIDDLE  ALT=\"cot%28x%29+=+cos%28x%29%2Fsin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "With that in mind, we can compute the cotangent value.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot%28A%2BB%29+=+cot%2890%29 ALIGN=MIDDLE  ALT=\"cot%28A%2BB%29+=+cot%2890%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace A+B with 90.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot%28A%2BB%29+=+cos%2890%29%2Fsin%2890%29 ALIGN=MIDDLE  ALT=\"cot%28A%2BB%29+=+cos%2890%29%2Fsin%2890%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use equation (1).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot%28A%2BB%29+=+0%2F1 ALIGN=MIDDLE  ALT=\"cot%28A%2BB%29+=+0%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use the unit circle to compute cos(90) and sin(90).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot%28A%2BB%29+=+0 ALIGN=MIDDLE  ALT=\"cot%28A%2BB%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Final answer.<BR>\n" );
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